Question

The eccentricity of the hyperbola $25x^2-9y^2-=225$ is ...

• A. $\frac{\sqrt{34}}{3}$
• B. $4$
• C. $\sqrt{34}$
• D. $\frac{\sqrt{34}}{5}$

Answer 1

Answer: (A)

We have equation of hyperbola
$25x^2-9y^2=225$
$\Rightarrow \frac{x^2}{9}-\frac{y^2}{25}=1$
On comparing with $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,$ we get
$a^2=9,b^2=25$
$\therefore$ Eccentricity, $e=\sqrt{1+\frac{b^2}{a^2}}$
$=\sqrt{1+\frac{25}{9}}$
$=\frac{\sqrt{34}}{3}$